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In this paper, the original discrete unified gas kinetic scheme (DUGKS) isextended to arbitrary Lagrangian-Eulerian (ALE) framework for simulating thelow-speed continuum and rarefied flows with moving boundaries. For ALE method,the mesh moving velocity is introduced into the Boltzmann-BGK equation. Theremapping-free scheme is adopted to develop the present ALE-type DUGKS, whichavoids the complex rezoning and remapping process in traditional ALE method. Asin some application areas, the large discretization errors will be introducedinto the simulation if the geometric conservation is not guaranteed. Threecompliant approaches of the geometric conservation law (GCL) are discussed anda uniform flow test case is conducted to validate these schemes. To illustratethe performance of present ALE-type DUGKS, four test cases are carried out. Twoof them are the continuum flow cases, which are the flows around theoscillating circular cylinder and the pitching NACA0012 airfoil, respectively.Others are the rarefied flow cases, one is the moving piston driven by therarefied gas, another is the flow caused by the plate oscillating in its normaldirection. The results of all test cases are in good agreement with the othernumerical and/or experimental results, demonstrating the capability of presentALE-type DUGKS to cope with the moving boundary problems at different flowregimes.

An ALE-type discrete unified gas kinetic scheme for low-speed continuum and rarefied flow simulations with moving boundaries